达尼尔积分的富比尼定理

Pub Date : 2024-04-09 DOI:10.1007/s00013-024-01988-w

Götz Kersting, Gerhard Rompf

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引用次数: 0

摘要

我们证明，在丹尼尔积分理论中，迭代积分总是可以形成的，积分的顺序总是可以互换的。通过这种方法，我们讨论了积积分，并证明相关的富比尼定理在一般情况下完全成立。这些结果建立在弗雷姆林（Fremlin）提出的关于里兹张量乘积的密度定理和富比尼-斯通（Fubini-Stone）定理的基础之上。

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Fubini’s theorem for Daniell integrals

We show that in the theory of Daniell integration iterated integrals may always be formed, and the order of integration may always be interchanged. By this means, we discuss product integrals and show that the related Fubini theorem holds in full generality. The results build on a density theorem on Riesz tensor products due to Fremlin, and on the Fubini–Stone theorem.

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